Probability and Venn Diagrams

Mutually Exclusive Events

Sample Space Diagrams

Probability Experiment

Probability Trees

Union and Intersection of Sets

Conditional Probability

Expectation and Mutually Exclusive Events

Venn Diagrams and Set Notation

Probability Trees and Independent Events

Conditional Probability

Prerequisite Knowledge

• Compare and order fractions whose denominators are all multiples of the same number
• Identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths
• Add and subtract fractions with the same denominator and denominators that are multiples of the same number

Success Criteria

• Record describe and analyse the frequency of outcomes of probability experiments using tables and frequency trees
• Apply ideas of randomness, fairness and equally likely events to calculate expected outcomes of multiple future experiments
• Relate relative expected frequencies to theoretical probability,
• Apply the property that the probabilities of an exhaustive set of outcomes sum to one; apply the property that the probabilities of an exhaustive set of mutually exclusive events sum to one
• Understand that empirical unbiased samples tend towards theoretical probability distributions, with increasing sample size
• Enumerate sets and combinations of sets systematically, using tables, grids, Venn diagrams and tree diagrams
• Construct theoretical possibility spaces for single and combined experiments with equally likely outcomes and use these to calculate theoretical probabilities
• Calculate the probability of independent and dependent combined events, including using tree diagrams and other representations, and know the underlying assumptions

Key Concepts

• When writing probabilities as a fraction using the probability scale to show equivalences with the keywords
• Discuss the effect of bias and sample size when comparing theoretical and experimental probabilities.
• Use the random function on a calculator or spreadsheet to demonstrate simple randomisation.
• When listing the outcomes of combined events ensure students use a logical and systematic method.
• Branches on a probability tree have a sum of one as they are mutually exclusive.
• Conditional probability is where the outcome of a future event is dependent on the outcome of a previous event.

Common Misconceptions

• Writing probabilities as a ratio is a common misconception.
• When creating Venn diagrams students often forget to place the remaining events outside the circles.
• When listing permutations of combined events students often repeat events when they do not use a logical and systematic method.
• Students often have difficulty completing Venn diagrams involving 3 intersecting circles.